Chapter 6 Waves and Sound
By Ray Merry
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Waves in Action:
A Longitudinal Wave, (similar to sound in air)
Wave

A traveling disturbance consisting of
coordinated vibrations that carry energy
with no net movement of matter.
See pages 217,218,219
Do the Wave!

Have you ever "done the wave" as part of a large
crowd at a football or baseball game? A group of
people jump up and sit back down, some nearby
people see them and they jump up, some people further
away follow suit and pretty soon you have a wave
traveling around the stadium. The wave is the
disturbance (people jumping up and sitting back
down), and it travels around the stadium. However,
none of the individual people the stadium are carried
around with the wave as it travels - they all remain at
their seats.
Wave medium
The wave medium is the substance the wave
is traveling through.
 E.G. Sound requires a media or material to
travel through. The media can be water,
air, wood, etc.
 Light on the other hand travels through a
vacuum, and may not require a media.

Compare a wave pulse and
a continuous wave.
A wave pulse is one up and down or back
and forth motion of a wave (short and
fleeting).
 A continuous wave has many pulses (steady
and repeating) .

Wave Pulse
Demonstrate both
transverse and longitudinal
waves on a Slinky,


Transverse wave
oscillations are perpendicular (transverse) to the
direction the wave travels. (p. 219 fig. 6.4 a.)
Longitudinal wave
oscillations are along the direction the wave travels. (p.
219 fig. 6.4 b.) note corrections in book p. 219 & 220
Examples of Waves and Their Type


Longitudinal,
Sound in air
Transverse, fan
wave, sea wave.
Speed of a wave on a rope depends on its
mass density and the tension applied.
 = greek letter rho, stands for linear density
= linear mass density of a rope, string, etc.
= m/l (mass/length)
 v= (F/)½ (Speed of a wave on a rope, etc.
= sq. rt. of Force/linear density.)

Compute the speed of sound in
air given the temperature.
V= 20.1x(T)1/2 (20.1 x sq.rt of Temp in
Kelvins)
 Speed of sound waves in air at
temperature T (SI units, T in Kelvins)

Wavelength and Amplitude




Amplitude: Maximum displacement of
points on a wave, measured from the
equilibrium position.
Wavelength: () The distance between two
successive "like" points on a wave.
An example is the distance between two
adjacent peaks or two adjacent valleys.
See fig.6.5 p221
Wavelength vs Amplitude Figure
l
Crest

Wavelength
A
A - Amplitude
Trough
Frequency of a Wave
The number of cycles of a wave passing
a point per unit time.
 It equals the number of oscillations per
second of the wave.
 If 15 waves pass a point in 1 second the
frequency f = 15 Hz.

Wave Equation
Equation relating the velocity, v,
frequency, f, and wavelength, , of a
continuous wave.
 V=f
 velocity of waves = frequency x
wavelength

Wavefronts and Rays.

See p 225 fig. 6.11 & fig 6.12 and p 226
fig. 6.14
The Red circle
represents wave front
Ray representing
direction of travel
of the wave
Amplitude of a wave gets smaller
farther from the source.
The wave energy spreads out in 3
dimensions, like the surface of a
sphere.
 As a result the same energy is
spread out over a larger and larger
surface and amplitude decreases.
Define a plane wave.

A wave so far from it’s source that the wave
front appears to be a straight line.
Give concrete examples of
reflection of waves.

Echoes.

Parabolic Antennas
Doppler effect

The apparent change in frequency of a
wave due to motion of the source of the
wave, the receiver, or both.
Effects of Movement on f and λ
If the source is moving towards the
observer, the observer perceives sound
waves reaching him or her at a more
frequent rate (high pitch)
 If the source is moving away from the
observer, the observer perceives sound
waves reaching him or her at a less frequent
rate (low pitch).

Consequences of the
Doppler effect.



pitch of an ambulance or police siren, goes
up as it approaches and then goes down as it
recedes from you
Same effect from a passing train whistle.
Used in astronomy to deduce the component
of velocity in the line-of-sight of an
approaching or receding planet/star/galaxy
etc.
How it was discovered that
the universe is expanding.
Doppler effect was used to determine speed
of galaxies.
 They were all found to be moving away
from the center
 The farther away they were the faster they
seemed to be going away!

Cosmology

The study of the structure and evolution
of the universe as a whole.
Hubble relation (or law)

A mathematical expression showing that
the farther a galaxy is from us, the
faster it is moving away. One implication
of this relation is that the universe is
expanding.
Echolocation: Radar, Sonar…
Process of using the reflection of a
wave to locate objects.
 We send out a wave, wait for its return.
 Since we know the speed and the time,
from d=v x t we determine its distance
away

Explain what causes a sonic
boom.
Sound waves build up in front as plane, etc.
approaches the speed of sound. When it
passes the speed of sound they are left
behind.
 Similar to bow waves on a boat.

Diffraction
The bending of a wave as it passes
around the edge of a barrier.
 Diffraction causes a wave passing
through a gap or a slit to spread out
into the shadow regions.
 See fig. 6.26 p. 232

Examples of Diffraction
Sound waves traveling around
corners
 Water waves going through
openings.

Interference


The
consequence
of two waves
arriving at the
same place
and
combining.
See fig. 6.28 p.
233
Constructive interference


occurs
wherever the
two waves
meet in phase
(peak matches
peak);
the waves add
together.
Destructive interference

Destructive interference occurs
wherever the two waves meet out of
phase (peak matches valley); the waves
cancel each other.
Phase and Interference
Give an explanation of how the phase
relationship of superposed waves
determines whether they interfere
constructively or destructively.
 In phase is constructive, out of phase 180
degrees (half a cycle) is destructive.

What is sound?
A wave disturbance which our ears are
sensitive to. A longitudinal wave in air, if it
is audible it has a frequency between 20 and
20,000 hz.
 Does sound occur if there is no one to hear
it?

Sound

The back and forth vibrations of the surrounding air
molecules creates a pressure wave which travels
outward from its source. This pressure wave consists
of compressions and rarefactions. The compressions
are regions of high pressure, where the air molecules
are compressed into a small region of space. The
rarefactions are regions of low pressure, where the
air molecules are spread apart. This alternating
pattern of compressions and rarefactions is known as
a sound wave.
Sound From a String
A sound wave is produced by a vibrating
object.
As a guitar string vibrates, it sets
surrounding air molecules into vibrational
motion.
The frequency at which these air
molecules vibrate is equal to the
frequency of vibration of the guitar string.
Reaction of the Air
The back and forth vibrations of the surrounding
air molecules creates a pressure wave which
travels outward from its source. This pressure
wave consists of compressions and
rarefactions.
Sound Wave
• The compressions are regions of high
pressure, where the air molecules are
compressed into a small region of space.
• The rarefactions are regions of low pressure,
where the air molecules are spread apart.
• This alternating pattern of compressions and
rarefactions is known as a sound wave.
Pitch
How high or low a sound is, related to the
frequency of the sound.
 Higher pitches have higher frequency
waves.

Decaying
Sound
• Frequency (F)
• Initial Amplitude (Amax)
• Halving Time (T½)
Reverberation
Ultrasound
Very high frequency sound waves,
higher than we can hear.
 Used in medicine in imaging and to
destroy kidney stones in the bladder

Applications of Sound
Sonar
 Ultrasound Analysis
 Bats Echolocation
 Insect Repellant/Dog Whistle

Musical Scale



8 notes in the
scale, key is the
starting note
Key of C has
CDEFGAB
Notes repeat in
octaves.
One octave is
double the
frequency of
the one below.
Pure tones, complex tones,
and noise.
Beats
Waves close in frequency sometimes
constructively interfere, causing a
sudden loudness.
 E.G. sound of 500 hz and 502 hz, 2 hz
is the difference or beat frequency,
502 –500 = 2
 Two times per second they would
interfere constructively.

Musical Instruments

Recognize some differences in the
ways various musical instruments
produce sound.
 wind instruments: blow reed vibrates
 percussion: stike and they vibrate
 strings: pluck or bow and they vibrate
Harmonics
Harmonics are sounds emitted in simple
ratios of the main or fundamental frequency
 First Harmonic or fundamental = f
 Second H = 2f
 Third H= 3f, etc.

1st
Harmonic
Diagrams
2nd
Sum
Standing Wave Demo

http://id.mind.net/~zona/mstm/physics/wave
s/standingWaves/standingWaves1/Standing
Waves1.html
Superposition of Waves

Problem on Harmonics
If a sound of A has 220 Hz, what are the
first and third harmonics?
 1st H = f = 1 x 220 = 220 Hz
 2nd H = 2 x f,
 third = 3 x f = 3 x 220 = 660Hz

Loudness and Decibels
A bel is a rating of the power of 10 of the
amplitude of a wave. E.g. 10, vs 100, = 1
bel more (101 vs. 102 ) which is 10 decibels
 Related to intensity of the sound. Closest
measurement is the decibel (.1 bel)
 Minimum difference in intensity we can
hear is 1 db, to sound louder

Decibel Ratings






120 db is the threshold of pain
2 identical sounds are 3 db higher than the single
sound.
It takes 10 identical sounds to sound twice as loud,
which is a change of 10 db.
This is cumulative, 100 db sounds 4x as loud as 80
db.
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